Traditional techniques to evaluate the efficiency to innovate of economic sectors face two difficulties: heterogeneous sectors, and uncertain and imprecise information. In this article, a methodology is proposed to deal with these conditions in a set of Brazilian economic sectors. Heterogeneity is addressed through a multicriteria sorting technique to assign sectors into categories of innovativeness. Next, deterministic, stochastic (SMAA-D and bootstrap) and fuzzy DEA methods are used to calculate efficiency scores inside each category in contexts of crisp, uncertain and imprecise data, respectively. Robustness analysis is undertaken to identify robust-efficient sectors. Necessarily and possibly efficient sectors are defined to analyze non-efficient units. Three groups can be recommended to policy-makers: sectors that do not need improvement actions to enhance efficiency; sectors that need improvement in their efficiency to innovate; and sectors that could need radical changes to improve their efficiency to innovate. Limitations are mentioned and future research is suggested.